Detectives investigating the murder of Joanna Yeates are facing criticism that they appear no closer to finding her killer and may have made errors during the early part of the inquiry.

Police admit they still do not know where and when the landscape architect died or at what stage her body was dumped on a roadside verge, and appear to have backtracked on a crucial early theory about how the killer may have got to her. Officers had been adamant there was no sign of a break-in at the flat, but now say they are following that line of inquiry.

Today, 10 days after Yeates's body was found and a week into the murder hunt, police launched a pop-up advert on Facebook to try to prompt more witnesses to come forward.

Forensic experts, some wearing breathing apparatus because hazardous chemicals were being used, continued to carry out tests at Yeates's flat in the Clifton area of Bristol. Police were also spotted in the home of her landlord, Chris Jefferies, who was arrested on suspicion of her murder and remains on police bail.

There were also unconfirmed reports tonight that police had brought in a criminal profiler to assist the investigation.

Meanwhile a new, grainy CCTV image emerged of a woman who could be Yeates on the night she disappeared. Two other figures were around 50 metres behind her – but the suggestion by the tabloid newspaper that published the image – taken from a pub CCTV system – that the pair may be suspects is being played down by the police.

However, there is impatience that there has been no breakthrough. Clifton ward councillor Trevor Blythe said: "People are afraid to go out at night and are taking extra precautions at home. Clearly the person or people who did this are still around. The police don't appear to have any leads at all. Everyone wants it resolved so we can get back to normal life. It could well be that the perpetrator knew the victim so it doesn't seem like a serial killer – but we just don't know."

An Avon and Somerset police authority member, who asked not to be named, said it was "worrying" that the police did not appear close to finding the murderer.

Concern has focused on the early days of the investigation. Yeates vanished from her flat in Canynge Road on 17 December. Her disappearance was reported on 19 December by her boyfriend, Greg Reardon, and it remained a missing person's inquiry until the body was found on Christmas morning.

Three days later a postmortem confirmed Yeates had been strangled, at which point Avon and Somerset's major crime investigation unit and Detective Chief Inspector Phil Jones, who has more than 20 years' experience, took charge.

Hitting back at suggestions there were delays in the inquiry, police insist they searched Yeates's flat "shortly" after she was reported missing and have kept it secure since then. But it was not until the murder hunt was formally launched that very detailed forensic work started. On the day it was confirmed that Yeates had been murdered, there was no continuous uniformed police guard outside the flat. The arrest of Yeates's landlord, Chris Jefferies, is a puzzle. He was seized shortly after the media carried claims attributed to him that he had seen three people leaving Yeates's flat – though police knew what he was saying for some time before the "sighting" was publicised.

Jefferies's flat was searched after his arrest on 30 December, five days after the body was found and 13 days after Yeates disappeared. Police say Jefferies remains a suspect and insist his arrest was made at the "appropriate time".

A crucial line for the police remains what happened to the pizza Yeates bought just before she vanished and its packaging. Officers are sifting through almost 300 tonnes of domestic rubbish in search of it. They seized the bin at Yeates's flat on 20 December but did not take the bins from the rest of the street until 23 December.

There have been mixed messages about the threat to residents in Clifton. Police have been saying they had no "specific intelligence" of an increased risk and strongly suggested that a random killer was not on the prowl. But they are now saying it is possible that more than one person was involved in the killing and are not ruling out a sexual motive.

Police insist the investigation is under control. One source pointed out that forensic test results take time to come through. Studying CCTV camera footage is also time-consuming – so far they have only looked through about 100 hours – a fraction of the available footage.

Yeates's mother, Theresa, today described how quiet life was without the 25-year-old. "She just had this joy and vibrancy, even though she didn't live here. I am sat in the kitchen just wanting her to come through the door. It is just so quiet here without her," she said.